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Appendix D
What to do in School and Why
Previous: C How to Read
A Why Go or Attend
Education is for both sons and daughters. The assumption that someone else
will provide home and shelter for us is too often false. So you should get the
most out of your schooling and education. Your ability to get a job, your future
earnings and your future joys and companions may all depend on what you learn in
and after school. All this may also depend on factors beyond your control (wars,
social conditions, the economy or parents). The suggestions provided below are
for some, not all eventualities.
School can be a place where you learn to master rule and pattern-based
thought (logic) and where you master further skills and knowledge. You are in
school to learn about the wide range of human knowledge and behavior. Try to
understand whatever you might be asked to study or do. Think for yourself and
ask why you or others do this or that.
In school, you should look for the ideas new to you and for the ideas worth
repeating to others. That is what makes a class or a subject worthwhile. Again,
ideas which you have already seen are reassuring and comforting - not much work
is needed here, but you only learn from the ideas new to you. Look and search
for them.
What you see in school and in books represents the experience of others. When
you are observant, you can learn from the experience, skills and mistakes of
others instead of your own.
History courses, English (or literature) courses, science courses and some
realistic novels offer this experience secondhand. Secondhand knowledge of
hardship is preferable to first hand. Ask your teachers, relatives and the
others about the joys and the difficulties they met or foresee. Learn from their
experience. Ask for opinions. Guidance from others requires the statement of
opinions. Get two or more opinions even if you liked the first. Seek and
politely allow opinions different from your own. Different points of view may
sharpen or change yours.
B Health and Social Skills
You are also in school to meet people and to learn how to mix or socialize
with others. To this end, join a club or group activity. See how people,
including yourself behave in groups. After school, the opportunities to mix may
decline - or you may not develop the habit of mixing and socializing. Choose
activities you like. Try one, two or several, but leave enough time for your
studies and for special events. Suggestion: each week, get three or more hours
of physical exercise. This exercise could come from physical labor. Or, you may
find a sport or activity which you can do now and later. This exercise should
build your health without risking it and without damaging it.4
4I
saw in a university soccer match or practice in 1984, a player with a small
cast on his leg. I thought he was risking permanent damage.
In 1990, after twenty years of cross-country skiing for exercise etc, I began
to ski in colder and colder conditions without fear. The eventual result was a
deep frostbite to my cheeks, an area difficult to protect. Then for five
years, exposure to the cold was an unpleasant experience followed by hours of
pain or discomfort - a distraction from work and play that is not recommended.
C Suggestions for Learning
By law you are required to attend school. Make sure your time is not wasted.
Make sure that some of your courses are with helpful, hard-driving, teachers.
Ask them for advice on what to do or what could be useful to you. Further advice
follows. It repeats in part advice given in previous appendices.
- Look for the ideas new to you and for ideas worth repeating. When you are
preparing for a test or for a future lesson, your studying is done when you
can find no ideas new to you.
- Try to remember the names of places, people and ideas. You can use the
names in conversations, essays and tests later.
- Learn to read precisely what is written. This skill will serve you well.
It gives you more independence both in class and when you leave school. It
may allow you to learn at your own pace.
- Learn to take notes. When no textbook is present, note-taking skills will
be needed. When a textbook is present, look at it first. (Reading it in
advance may allow you to take fewer notes and understand lessons better.)
- Learn to type. Today, computers are used in all areas of office work
bureaucracy and technology. These computers are controlled by keyboards.
Accurate, if not fast, typing skills will make your exposure to computers
and report writing more pleasant.5
5This
advice is valid now. Advances in computer technology - the introduction of
voice-controlled dictation/computer systems - may make part of this advice
stale or obsolete.
- Get careful thinking skills. That is, master the use of rules and
patterns. Every area of skill and knowledge offers rules and patterns which
you might follow. Learn to read exactly what each says. To follow, to agree
or to disagree with rules, you need to understand exactly what they say and
exactly what they don't say.
- In high school take courses which provide immediate job skills such as
auto-mechanics, typing, metalwork, woodwork, drafting etc. Master arithmetic
and learn to read and write carefully. Employers want skilled workers. They
are easier to train and worth keeping. Even if you are planning a college
education, practical job skills could get you a summer job. They may allow
you to work and pay for part of a college education. Care is required to
take the best and avoid the worst of the academic and non-academic courses
in your school.
- Take English or master another language of your choice, well. This
includes reading, writing, speaking and reasoning. When you write, tell a
story, describe what is, or present an opinion or defend one. Watching for
ideas worth repeating, will help.
- Take history courses. Courses with ideas new to you are worth taking. If
possible, avoid history courses which only promote the group, state or
country in which you live. History courses tell us about the experiences and
mistakes of past, if not present generations.
- Read newspapers which do not (always) glorify the nation or group to which
you belong. Contrary opinions make us think. So look for and read newspapers
with views you occasionally find disagreeable.
- A little uncertainty in the words of a teacher leaves room for thought and
the practice of thinking skills.
Appendices with (repetitive) advice for Students: [ B How to Learn ] [ C. How to Read ] [ D. What to do in School ] [ PS. Study Tips ] [ PS: Time and Effort ] [ E. How to Study Math and Why ]
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Three Skills
For
Algebra
Volume 2
Printed in Canada
ISBN 0-9697564-2-9
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Read slowly, this work may enrich your
skills & knowledge. Take the risk.
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Chapters and Appendices
B How to Learn C. How to Read D. What to do in School PS. Study Tips PS: Time and Effort E. How to Study Math and Why
Foreword 1. Introduction 2. Implication Rules [4] 3. Chains of Reason [3] 4. Induction Mathematical 4. Romeo and Juliet 6 Old Language 5 Knowledge Islands [2] 7 Arith Skill Check [4 X 2] Arith Webvideos 7. The Next Chapters 8 The Three Skills 8 VNR-Concise-Encyclopedia PS. What is a Variable [8] 9. Algebra Talk [7] 10 Two More Skills[5] 11 Why Shorthand 12 Shorthand Usage [10] 13 What's Next PS: The 4-th Skill For Algebra 14 Compound Interest [6] 15 Linear Equations [5] 16 Painless Proofs 17 Pythagoras PS I. Distributive Law PS II. Polynomials 18 Rules of Algebra [20] 19 Functions & Sets 20 Degrees & Radians 21 What's Next 22. Arith & Geometric Sums [2] 23 Summation Notation 24 Your Money [3] 25 Induction & Recursion [4] 26 What's Next 27 Pronouns in Logic 28 Occurrence Tables 29 Contrapositive 30 Truth Tables 31 Indirect Reason Pathways for Learning
What is a Variable?
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
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For
Senior
High School & Calculus Students
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Words to clearly
introduce algebra and variables
have been missing in course design. For people who cannot do
algebra,
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the missing words may
explain or ease their difficulties. Volume 2 ,Three
Skills for Algebra, in Chapters
8 to 14 & 18 etc, puts words before symbols to
providing the missing words in a way that enrich the
comprehension of all. Those words form the middle part of a algebra
(and logic) lessons aimed at helping or improving all
of high school mathematics and also calculus course
design & delivery.
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For Avid Readers in School & Out -
Online Books
1. Elements of
Reason. 1996
1A. Pattern
Based Reason 1995
1B. Math
Curriculum Notes 1996
2. Three
Skills for Algebra 1995
3.Why
Slopes & More.Math
1995
Tour their forewords.
Calculus Prep or Help: See Volumes 2 & 3,
and this bigger
Calculus
Guide. If your
calculus questions is not answered here, submit
it. Over time, that may complete the site development of
calculus.
For Parents: Speaking
Skills, Reading
& Writing,
Preparing for Science, ends,
values and methods for work and study, parent- friendly maths
skill development booklets for ages 4-14.
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Mostly
For High
School
Intro to Solving
Linear Equations
- a different paths for junior and even senior high
school students. Question for Tutors: When do
you use and when you skip the stick diagram method
here?
Fraction
Skills, thought-based development, Ages 10 to 14 may need a
tutor. Students who have to understand in order
to do may like the development in all or part.
For Senior
High School Mathematics & Calculus
5
wordy Logic
Chapters
4 curious Algebra
Chapters
Words before & besides symbols. A Key Algebra
forward & backwards Chapter
First Calculus
Preview (1st intro)
Four Calculus
Chapters
(2nd intro)
Intro to Complex
Numbers (long)
Intro to Mathematical
Induction (romantic & wordy at first)
Tutors & Instructors:
These lessons introduce skills differently Would you
recommend them?
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More Topics
1. Decimal
Arithmetic Reference!
2. Integers
- Intro to Signed No.s
3. Fractions
- fully explained.
4. Fractions
with Units
5. Number
Theory,
6. Solving
Linear Equations
7 Formulas
for- & backwards -
8. Proportionality,
Back- & For-wards.
9. Logic
Chapters:
10. Euclidean-Geometry
11. Slopes
& Equations of Straight Lines. (Take
I. See take II below)
12. Why
Study Slopes.
13. Maps,
Plans, Similarity & Trig,
(Take II included here)
14. Quadratics:
Starter lessons
15. Polynomials:
Starter lessons
16 Why
Factor Polynomials:
17 Functions
- Forwards & Backwards.
18. Exponents,
Radicals & logs.
19. Complex
Numbers before trig (new advance/ starter lesson)
20. DC
Electric
Circuits Etc
21. Real
Analysis
22. The
Olde Complex No, Trig
& Vector Section.
23. More
Calculus Stuff
- written after Volumes 2 and 3.
Level I Material: New Stuff
Time and Date Matters
Level I Arithmetic.
Money Matters
Measurement Matters
Matters of Chance (Risk Control)
Logic
Chapters
(leave what's not clear in Level I to Level II)
Using/Making Maps and Plans.
(A variant of
Maps,
Plans, Similarity & Trig, to
appear here).
For Instructors
-
Education
Essays
(opinions,
possibilities, references)
- Free
Advice and Directions for teaching primary & high school maths
will be given in online meeting place with voice &
whiteboard.
- Math & Logic How-TOs
1. Arithmetic
2. Algebra
3. More Algebra
4. Beginner Geometry
5. More Geometry
6. Calculus
7. Show Work or Logic
These may be too dense for students. Offering ideas to change
education makes this site different. Nothing
ventured, nothing gained. Site material is
mathematically correct, and where not, please report
errors. The two level program POMME in the site
entrance implies multiple paths for instruction. Supporting
those paths in turn implies a clear destination for
site development and perhaps a new name.
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